Question:
A city's population in 2025 is 1,75,000 and is expected to increase in the next three decades at a growth rate of 8.5% per decade. In 2055, the estimated per capita domestic water demand will be 175 litres per day. The total daily domestic water demand for the city in 2055 (in million litres per day) will be (rounded off to two decimal places).
A city's population in 2025 is 1,75,000 and is expected to increase in the next three decades at a growth rate of 8.5% per decade. In 2055, the estimated per capita domestic water demand will be 175 litres per day. The total daily domestic water demand for the city in 2055 (in million litres per day) will be (rounded off to two decimal places).
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Grow the 2025 population by 8.5% per decade for 3 decades (compound growth), then multiply by 175 lpcd and convert to MLD.
Updated On: Aug 6, 2026
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Verified By Collegedunia
Correct Answer: 39.12
Solution and Explanation
Step 1: Understanding the Question.
The city has a population of 1,75,000 in 2025. It grows at a rate of 8.5% every decade for the next three decades, taking us to the year 2055. We need the total daily domestic water demand in 2055, given a per capita demand of 175 litres per day.
Step 2: Find the population in 2055.
Since the growth rate is stated per decade, use the geometric (compound) growth method. If \(P_0\) is the population in 2025 and \(r\) is the decadal growth rate, the population after \(n\) decades is
\[ P_n = P_0 (1+r)^n \]
Here \(P_0 = 1,75,000\), \(r = 0.085\), and \(n = 3\) decades (2025 to 2055).
\[ (1.085)^3 = 1.085 \times 1.085 \times 1.085 = 1.27729 \]
So
\[ P_{2055} = 175000 \times 1.27729 = 223525.6 \text{ persons} \]
Step 3: Find the total daily water demand.
The per capita domestic water demand in 2055 is 175 litres per day. Multiply this by the projected population to get the total demand in litres per day.
\[ \text{Total demand} = 223525.6 \times 175 = 39{,}116{,}980 \text{ litres/day (approx)} \]
Step 4: Convert to million litres per day (MLD).
Divide by 10,00,000 to convert litres to million litres.
\[ \text{Total demand} = \frac{39116980}{1000000} = 39.12 \text{ MLD} \]
Final Answer:
The total daily domestic water demand for the city in 2055 works out to about 39.12 million litres per day. \[ \boxed{39.12 \text{ MLD}} \]
The city has a population of 1,75,000 in 2025. It grows at a rate of 8.5% every decade for the next three decades, taking us to the year 2055. We need the total daily domestic water demand in 2055, given a per capita demand of 175 litres per day.
Step 2: Find the population in 2055.
Since the growth rate is stated per decade, use the geometric (compound) growth method. If \(P_0\) is the population in 2025 and \(r\) is the decadal growth rate, the population after \(n\) decades is
\[ P_n = P_0 (1+r)^n \]
Here \(P_0 = 1,75,000\), \(r = 0.085\), and \(n = 3\) decades (2025 to 2055).
\[ (1.085)^3 = 1.085 \times 1.085 \times 1.085 = 1.27729 \]
So
\[ P_{2055} = 175000 \times 1.27729 = 223525.6 \text{ persons} \]
Step 3: Find the total daily water demand.
The per capita domestic water demand in 2055 is 175 litres per day. Multiply this by the projected population to get the total demand in litres per day.
\[ \text{Total demand} = 223525.6 \times 175 = 39{,}116{,}980 \text{ litres/day (approx)} \]
Step 4: Convert to million litres per day (MLD).
Divide by 10,00,000 to convert litres to million litres.
\[ \text{Total demand} = \frac{39116980}{1000000} = 39.12 \text{ MLD} \]
Final Answer:
The total daily domestic water demand for the city in 2055 works out to about 39.12 million litres per day. \[ \boxed{39.12 \text{ MLD}} \]
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